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transpose to the head of genes, except the root (insertion sequence elements
or IS elements); (2) short fragments with a function in the first position that
transpose to the root of genes (root IS elements or RIS elements); and (3)
entire genes that transpose to the beginning of chromosomes.
The existence of IS and RIS elements is a remnant of the developmental
process of GEP itself, as the first gene expression algorithm used only single-
gene chromosomes and, in such systems, a gene with a terminal at the root was
of little use. Consequently, transposition to the root was tightly controlled and
only transposons with a function in the first position were allowed to trans-
pose to the root. When multigenic chromosomes were introduced, this feature
was maintained as these operators not only serve different purposes in evolu-
tion but are also important to the understanding of the functions and the re-
quirements of the genetic operators. Indeed, the comparison of the transform-
ing power of these operators (see a discussion of The Genetic Operators and
Their Power in chapter 12) shows clearly that there is no need to be cautious
while designing genetic operators, rejecting everything that seems to give rise
to too drastic a modification. In fact, on its own, root transposition - undoubt-
edly the most disruptive operator in GEP - is capable of finding very good
solutions very efficiently. Moreover, IS and RIS transposition are also capable
of creating simple repetitive sequences in the genome and this, in itself, is not
only curious but also extremely important to an efficient evolution.
Transposition of IS Elements
Any sequence in the genome can become an IS element and, therefore, these
elements are randomly chosen throughout the chromosome. The transposon
is then copied at the place of origin and the copy is afterwards inserted at a
randomly chosen point in the head of a gene, except the start position. Thus,
the transposition operator randomly chooses the chromosome, the start and
termination points of the IS element, and the target site. Typically, a small IS
transposition rate
p
is
of 0.1 is used as this operator is seldom used as the only
source of genetic variation.
The workings of IS transposition can be analyzed in the evolutionary his-
tory presented in Figure 3.18. As an illustration, and because only IS trans-
position is being used to create genetic diversity, a much higher transposi-
tion rate of 1.0 was chosen. And as you can see, by itself, this operator can
also make populations evolve and find good solutions to the problem at hand.
Indeed, chromosome 8 of generation 13 is a perfect solution to the majority
function problem.
